Fuzzy c-mean (FCM) is one of the widely used data clustering methods. FCM method not only divides a data set into several clusters but also determines the potential belongingness of each data in different clusters. The size of clusters generated by FCM cannot be controlled by the inherent mechanism. However,sometimes real life situations demand that the clusters should have some pre-specified size. In this study, the FCM method is further extended to obtain clusters with specified size. In the first step of the proposed method, FCM algorithm is executed; later the potential belongingness matrix passes through an optimization model to yield clusters with specified sizes. In the proposed technique, the centres of the clusters obtained from FCM are considered but the boundary elements are redistributed to achieve equal or custom-sized clusters. The methodology has been explained further with examples.

This paper considers a shortest path problem in an imprecise and random environment. The edges in the network represent the approximate time required to cover the distance from one vertex to another vertex while the traffic conditions change randomly for each edge. The approximate time has been defined by using trapezoidal fuzzy number whereas the traffic conditions has been defined in linguistic term. Such type of network problem can be called as Fuzzy Stochastic Shortest Path Problem (FSSPP) in imprecise and random environment. In order to solve the model, a method has been proposed based on the Dijkstra’s algorithm and some numerous example have been solved to present its effectiveness

In this article, we study a continuous-review production-inventory model that assembles lost sales and backorders with service level constraint. The study under consideration assumes that the distribution of demand during the lead-time is known partially. The objective of this paper is twofold. Firstly, the distributionfree procedure is applied to obtain a closed-form solution of optimal production quantity, re-order level and lead-time in the random framework. Secondly, considering demand as a fuzzy random variable, the procedure isextended to the fuzzy random framework in which an algorithm is proposed to find the optimal global solution. Two numerical examples are provided to illustrate the methods. Furthermore, sensitivity analysis is performed to present some managerial inferences